Bollettino dell'Unione Matematica Italiana

, Volume 11, Issue 1, pp 31–38 | Cite as

A note on gonality of curves on general hypersurfaces

  • Francesco Bastianelli
  • Ciro Ciliberto
  • Flaminio FlaminiEmail author
  • Paola Supino


This short paper concerns the existence of curves with low gonality on smooth hypersurfaces \(X\subset \mathbb {P}^{n+1}\). After reviewing a series of results on this topic, we report on a recent progress we achieved as a product of the Workshop Birational geometry of surfaces, held at University of Rome “Tor Vergata” on January 11th–15th, 2016. In particular, we obtained that if \(X\subset \mathbb {P}^{n+1}\) is a very general hypersurface of degree \(d\geqslant 2n+2\), the least gonality of a curve \(C\subset X\) passing through a general point of X is \(\mathrm {gon}(C)=d-\left\lfloor \frac{\sqrt{16n+1}-1}{2}\right\rfloor \), apart from some exceptions we list.


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© Unione Matematica Italiana 2017

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di BariBariItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di Roma “Tor Vergata”RomaItaly
  3. 3.Dipartimento di Matematica e FisicaUniversità degli Studi “Roma Tre”RomaItaly

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